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   "outputs": [],
   "source": [
    "'''\n",
    "线性回归的从零开始是实现\n",
    "使用NDArray和autograd来实现一个线性回归的训练\n",
    "'''\n",
    "%matplotlib inline\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "from mxnet import autograd, nd\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "生成数据集\n",
    "训练数据集样本数为1000，输⼊个数（特征数）为2\n",
    "我们使⽤线性回归模型真实权重w = [2, −3.4]^T 和偏差 b = 4.2\n",
    "以及一个随机噪声项来生成标签\n",
    "噪声项服从均值为0、标准差为0.01的正态分布。\n",
    "'''\n",
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2, -3.4]\n",
    "true_b = 4.2\n",
    "features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))\n",
    "labels = true_w[0] * features[:,0] + true_w[1] * features[:,1] + true_b\n",
    "labels += nd.random.normal(scale=0.01, shape=labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "(\n",
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       " <NDArray 2 @cpu(0)>,\n",
       " \n",
       " [4.879625]\n",
       " <NDArray 1 @cpu(0)>)"
      ]
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     "execution_count": 4,
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   "source": [
    "features[0], labels[0]"
   ]
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  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "'''\n",
    "通过生成第二个特征features[:,1]和标签labels的散点图\n",
    "可以更直观的观察两者之间的线性关系\n",
    "'''\n",
    "def use_svg_display():\n",
    "    # 用矢量图显示\n",
    "    display.set_matplotlib_formats('svg')\n",
    "def set_figsize(figsize=(3.5, 2.5)):\n",
    "    use_svg_display()\n",
    "    # 设置图片的尺寸\n",
    "    plt.rcParams['figure.figsize'] = figsize\n",
    "\n",
    "set_figsize()\n",
    "plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1); # 加分号只显示图"
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "读取数据集\n",
    "读取小批量数据样本\n",
    "函数作用：它每次返回batch_size（批量⼤小）个随机样本的特征和标签。\n",
    "'''\n",
    "# 本函数已经保存在d2lzh包中方便以后使用\n",
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices)\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = nd.array(indices[i:min(i+batch_size, num_examples)])\n",
    "        yield features.take(j), labels.take(j) # 根据take函数索引返回对应元素"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[[ 1.1756743   0.5103031 ]\n",
      " [-0.68288445 -0.25153375]\n",
      " [-1.4699515  -0.56158173]\n",
      " [ 0.29963878 -1.804639  ]\n",
      " [ 1.3891097  -0.93674135]\n",
      " [-0.96258074  1.0641294 ]\n",
      " [ 0.498848    0.44148442]\n",
      " [-1.3342137   0.9501345 ]\n",
      " [-0.4917022   0.5101816 ]\n",
      " [ 0.53874415  0.08753639]]\n",
      "<NDArray 10x2 @cpu(0)> \n",
      "[ 4.815456   3.6914947  3.1684966 10.940572  10.165997  -1.3526626\n",
      "  3.6817775 -1.6872916  1.4843812  4.9876847]\n",
      "<NDArray 10 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "初始化模型参数\n",
    "权重初始化成均值为0、标准差为0.01的正态随机数，偏差则初始化成0\n",
    "'''\n",
    "w = nd.random.normal(scale=0.01, shape=(num_inputs, 1))\n",
    "b = nd.zeros(shape=(1,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 求梯度\n",
    "w.attach_grad()\n",
    "b.attach_grad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "定义模型\n",
    "'''\n",
    "def linreg(X, w, b):\n",
    "    return nd.dot(X, w) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "定义损失函数\n",
    "'''\n",
    "def squared_loss(y_hat, y):\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "定义优化算法\n",
    "sgd函数实现了上⼀节中介绍的小批量随机梯度下降算法\n",
    "通过不断迭代模型参数来优化损失函数\n",
    "'''\n",
    "# lr:学习率\n",
    "def sgd(params, lr, batch_size): \n",
    "    for param in params:\n",
    "        param[:] = param - lr * param.grad / batch_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.035136\n",
      "epoch 2, loss 0.000122\n",
      "epoch 3, loss 0.000049\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs): # 训练模型一共需要 num_epochs 个迭代周期\n",
    "    # 在每一个迭代周期中，会使用训练数据集中所有样本一次（假设样本能够被批量大小整除）\n",
    "    # X和y分别是小批量样本的特征和标签\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        with autograd.record():\n",
    "            l = loss(net(X, w, b), y)  # l是有关小批量X和y的损失\n",
    "        l.backward() # 小批量的损失对模型参数求梯度\n",
    "        sgd([w, b], lr, batch_size) # 使用小批量随机梯度下降迭代模型参数\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().asnumpy()))\n",
    "        "
   ]
  },
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   "cell_type": "code",
   "execution_count": 25,
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